1. Managing Inventory throughout the Supply Chain

2. Chapter Objectives Be able to:
Describe the various roles of inventory, including the different types of inventory and inventory drivers.
Distinguish between independent demand and dependent demand inventory.
Calculate the restocking level for a periodic review system.
Calculate the economic order quantity (EOQ) and reorder point (ROP) for a continuous review system.
Determine the best order quantity when volume discounts are available.
Calculate the target service level and target stocking point for a single-period inventory system.
Describe how inventory decisions affect other areas of the supply chain. In particular, be able to describe the bullwhip effect, inventory positioning issues, and the impact of transportation, packaging, and material handling considerations.

3. Inventory Management Functions, forms, and drivers of inventory
Inventory cost issues
Tools: Economic order quantity (EOQ) Reorder point (ROP) and safety stock Dealing with quantity discounts

4. Types of Inventory Cycle stock Safety stock (buffer inventory)
Anticipation inventory
Others
Hedge inventories
Transportation inventory (pipeline)
Smoothing inventories

5. Four Inventory Drivers
Demand and Supply Uncertainties
Safety stock, hedge inventory
Demand and Process Volume Mismatches
Cycle stock
Demand and Capacity Mismatches
Smoothing inventory
Demand and Supply Lead-Time Mismatches
Anticipation inventory, transportation inventory

6. Independent Demand Demand from outside the organization
Unpredictable  usually forecasted
Demand for tables . . .

7. Dependent Demand Tied to the production of another item
Relevant mostly to manufacturers
Once we decide how many tables we want to
make, how many legs do we need?

8. Two “Classic” Systems for Independent Demand Items
Periodic review systems
Continuous (perpetual) review systems
Factors
Order quantity (Q)
Restocking level (R)
Inventory level when reviewed (I)

9. Restocking Levels Periodic Review Continuous Review Periodic Review
Here RP+L represents the reorder period plus the order lead time, mu is the average demand during that time and sigma is the standard deviation of the demand during that time.
Z or zeta is the number of standard deviations chosen to achieve a desired service level.
Continuous Review:
Here d is the demand rate and L is the lead time for an order to come in. Obviously, variations in the demand and lead time are not accounted for since continuous review allows adjustment for some variation in these values.

10. Periodic Review System (Orders at regular intervals)
Inventory
level 2 4 6
Time

11. Continuous Review System (Orders when inventory drops to R)
How is the reorder
point ROP established? Q
Inventory
level R
Time
L-T
lead time to get a new order in

12. Comparison of Periodic and Continuous Review Systems
Periodic Review
Fixed order intervals
Variable order sizes
Convenient to administer
Orders may be combined
Inventory position only required at review
Continuous Review
Varying order intervals
Fixed order sizes (Q)
Allows individual review frequencies
Possible quantity discounts
Lower, less-expensive safety stocks

13. Order Quantity Q and Average Inventory Level
As the order quantity doubles
so does the average inventory (= Q/2) Q2
Q2 2 Q1
Q1 2

14. What is the “Best” Order Size Q?
Determined by:
Inventory related costs
Order preparation costs and setup costs
Inventory carrying costs
Shortage and customer service costs
Other considerations
Out of pocket or opportunity cost?
Fixed, variable, or some mix of the two?

15. Economic Order Quantity (EOQ) Model
Cost Minimizing “Q”
Assumptions:
Uniform and known demand rate
Fixed item cost
Fixed ordering cost
Constant lead time

16. What are the Total Relevant Annual Inventory Costs?
Consider:
D = Total demand for the year
S = Cost to place a single order
H = Cost to hold one unit in inventory for a year
Q = Order quantity
Then:
Total Cost = Annual Holding Cost + Annual Ordering Cost
= [(Q/2) × H] + [(D/Q) × S]
Comment: Can explain to students that item cost is considered when evaluating volume discounts
How do these costs vary as Q varies?
Why isn’t item cost for the year included?

17. Holding Cost $
(Q/2)×H
Holding cost increases
as Q increases . . . Q

18. Ordering costs per year decrease as Q increases$
Ordering costs per year
decrease as Q increases
(why?)
(Q/2)×H
(D/Q)×S Q

19. Total Annual Costs and EOQ
EOQ at minimum total cost

20. EOQ Solution
When the order quantity = EOQ, the holding and setup costs are equal

21. Sample Problems
Pam runs a mail-order business for gym equipment. Annual demand for the TricoFlexers is 16,000. The annual holding cost per unit is $2.50 and the cost to place an order is $50. What is the economic order quantity?
Using the same holding and ordering costs as above, suppose demand for TricoFlexers doubles to 32,000. Does the EOQ also double? Explain what happens.
Answers: EOQ = 800; 1,131 (goes up by the square root of 2)

22. EOQ tells us how much to order...
…but when should we order?
Reorder point and safety stock analysis

23. Safety Stock
When both lead time and demand are constant, you know exactly when your reorder point is ... Q R L

24. Safety Stock II Under these assumptions:
Reorder point = total demand during the lead time between placement of the order and its receipt.
ROP = d × L, where
d = demand per unit time, and
L = lead time in the same time units

25. Safety Stock III (Uncertainties)
But what happens when either demand or lead time varies? Q R L1 L2

26. Safety Stock IV What causes this variance? Average demand
during lead time

27. Uncertainty Drivers The variability of demand
The variability of lead time
The average length of lead time
The desired service level
2) and 3) are determined by a company’s choice of supply chain partners

28. Safety Stock
Additional inventory beyond amount needed to meet “average” demand during lead time
Protects against uncertainties in demand or lead time
Balances the costs of stockouts against the cost of holding extra inventory

29. Shown Graphically …
Now, what is the
chance of a stockout? 7%
93%

30. Recalculating the Reorder Point to include Safety Stock

31. Determining “z”
z = number of standard deviations above the average demand during lead time
The higher z is:
The lower the risk of stocking out
The higher the average inventory level
What is the average inventory level when we include safety stock?
Average inventory plus safety stock level

32. Determining “z”
Typical choices for z: z =  90% service level z =  95% service level z =  99% service level
What do we mean by “service level”?

33. Reorder Point + Safety Stock Formula:
What happens if lead time is constant?
What happens if the demand rate is constant?
What happens if both are constant?
If you wanted to reduce the amount of safety stock you hold, what is your best option?

34. Problems I One of the products stocked by Sam’s Club is SamsCola.
During the slow season, the demand rate is approximately 650 cases a month, which is the same as a yearly demand rate of 650×12 = 7,800 cases.
During the busy season, the demand rate is approximately 1,300 cases a month, or 15,600 cases a year.
The cost to place an order is $5, and the yearly holding cost for a case of SamsCola is $12.

35. Problems II According to the EOQ formula:
How many cases of SamsCola should be ordered at a time during the slow season?
How many cases of SamsCola should be ordered during the busy season?
Slow season: 81 cases
Busy season: 114 cases

36. Problems III
During the busy season, the store manager has decided that 98 percent of the time, he does not want to run out of SamsCola before the next order arrives. Use the following data to calculate the reorder point for SamsCola.
Weekly demand during the busy season: 325 cases per week
Lead-time: 0.5 weeks
Standard deviation of weekly demand: 5.25
Standard deviation of lead-time: 0 (lead-time is constant)
Number of standard deviations above the mean needed to provide a 98% service level (z): 2.05
Answer: 170 cases

37. Quantity Discounts I What effect will quantity discounts have on EOQ?
D = 1,200 units (100×12 months)
H = $10 per unit per year
S = $30.00 ordering cost
Order Size Price
$35.00
90 and up $32.50
Note: When H is a cost based on a percent of the value of the item, these calculations become more complicated, but are done in the same way.

38. Quantity Discounts II 1. Calculate the EOQ for the non discount price:
2. If we can order this quantity AND get the lowest price, we’re done. Otherwise ...

39. Quantity Discounts III
Compare total holding, carrying, AND item cost for the year at:  Each price break  The first feasible EOQ quantity
Do you understand why we must now look at item cost for the year?

40. Quantity Discounts IV Total costs at an order quantity of 85:
(85/2)×$10 + (1200/85)×$ ×$35.00 =
$ $ $42,000 = ??
Total costs at an order quantity of 90:
(90/2)×$10 + (1200/90)×$ ×$32.50 =
$ $ $39,000 = ??
Quantity 85: $42,848.53
Quantity 90: $39,850

41. Conclusions:
When all costs are considered, it is cheaper to order 90 at a time and take the price discount.
When there are volume discounts, the EOQ calculation might be infeasible or might not result in lowest total cost.
If holding cost is a percentage of the item value (a common practice for more expensive items), analysis is more complex, but done the same way

42. Single-Period Inventory (When safety stock is not an option)
Inventory is perishable
Newspapers, periodicals
Fresh food, Christmas trees
Must balance costs of
Being short = profit lost
Having excess = item cost + disposal cost – salvage value
Requires a target service level that best balances shortage and excess costs

43. Target Service Level
Sets expected shortage cost = expected excess cost
Or (1–p) × Cshortage = p × Cexcess
Where p = probability of enough units to meet demand, (1–p) = probability of shortage
Hence solving for p where the top equation is true provides the target service level
SLT = Cshortage / (Cshortage + Cexcess)

44. Target Stocking Point Must know how demand is distributed
Is it roughly the same every day?
Are there different demand distributions?
In all cases, develop the cumulative probability distribution for the demand levels in order of increasing demand and select demand level whose corresponding cumulative probability is nearest to the target service level.

45. Text Example for SLT = 65%

46. Inventory in the Supply Chain
Bullwhip Effect
Small demand changes  large order variations
Inventory Positioning
Cost and value increases, flexibility decreases down the supply chain  where do we hold inventory?
Transportation, Packaging, Material Handling
Physical size and quantity of lot, how it is packaged, handling equipment needed,and disposal of packaging are all factors in choosing appropriate supplier and distribution process

47. Demand versus Order Size (Bullwhip Effect)

48. Case Study in Inventory Management
Northcutt Bikes: The Service Department

49. Supplement ABC Classification Method
IDEA
Companies have thousands of items to track
Methods like EOQ only justifiable for most important items.

50. ABC Method Determine annual $ usage for each item
Rank the items according to their annual $ usage
Let:
Top 20%  “A” items  roughly 80% of total $
Middle 30%  “B” items  roughly 15% of total $
Bottom “50%  “C” item  roughly 5% of total $

51. ABC Analysis Example Total $ Usage = $98,500 Item Cost Demand $ Usage
$46
200
$9,200 B2
$40 10
$400 C3 $5
6680
$33,400 D4
$81
100
$8,100 E5
$22 50
$1,100 F6 $6
$600 G7
$176
250
$44,000 H8
150
$900 I9
$10
$100
J10
$14
$700
Total $ Usage = $98,500

52. Ranking by Annual $ Usage
Item
$ Usage
Cumulative $ Usage
% of Total $ Usage
Class G7
$44,000
44.67% A C3
$33,400
$77,400
78.58% A1
$9,200
$86,600
87.92% B D4
$8,100
$94,700
96.14% E5
$1,100
$95,800
97.26% H8
$900
$96,700
98.17% C
J10
$700
$97,400
98.88% F6
$600
$98,000
99.49% B2
$400
$98,400
99.90% I9
$100
$98,500
100.00%